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{-# LANGUAGE TemplateHaskell #-} | |
{-# LANGUAGE TypeOperators #-} | |
{-# LANGUAGE MultiParamTypeClasses #-} | |
{-# LANGUAGE RankNTypes #-} | |
{-# LANGUAGE FlexibleInstances #-} | |
{-# LANGUAGE FlexibleContexts #-} | |
{-# LANGUAGE UndecidableInstances #-} | |
{-# LANGUAGE GADTs #-} | |
module Main (main) where | |
import Data.Comp.Multi | |
import Data.Comp.Multi.Show () | |
import Data.Comp.Multi.Equality () | |
import Data.Comp.Multi.Ordering () | |
import Data.Comp.Multi.Derive | |
import Data.Comp.Multi.Ops | |
data Value e l where | |
Const :: Int -> Value e Int | |
Pair :: e i -> e j -> Value e (i,j) | |
data Op e l where | |
Add, Mult :: e Int -> e Int -> Op e Int | |
Fst :: e (i,j) -> Op e i | |
Snd :: e (i,j) -> Op e j | |
type Sig = Op :+: Value | |
$(derive [makeHFunctor, makeHFoldable, makeHTraversable, makeShowHF, makeEqHF, | |
makeOrdHF, smartConstructors, smartAConstructors] | |
[''Value, ''Op]) | |
simplify :: Term Sig :-> Term Sig | |
simplify = transform simplifyTf | |
where simplifyTf :: Term Sig :-> Term Sig | |
simplifyTf t = case unTerm t of | |
Inl t' -> op t' | |
Inr _ -> t | |
op :: Op (Term Sig) :-> Term Sig | |
op t@(Add t' t'') | t' == t'' = iMult (iConst 2) t' | |
| otherwise = inject t | |
op t = inject t | |
class Simplify f where | |
simplifyCoa :: CVCoalg f (Term f) | |
simplify' :: (HFunctor f, Simplify f) => Term f :-> Term f | |
simplify' = futu simplifyCoa | |
instance Simplify Sig where | |
simplifyCoa = simplifyCoa' | |
where simplifyCoa' :: CVCoalg Sig (Term Sig) | |
simplifyCoa' t = case unTerm t of | |
Inl t' -> op t' | |
t'@(Inr _) -> hfmap Hole t' | |
op :: forall l. Op (Term Sig) l -> Sig (Context Sig (Term Sig)) l | |
op t@(Add t' t'') | t' == t'' = Inl (Mult (iConst 2) (Hole t')) | |
| otherwise = Inl (hfmap Hole t) | |
op t = Inl (hfmap Hole t) | |
exs :: [E (Term Sig)] | |
exs = [E (iAdd (iConst 1) (iConst 1)), | |
E (iAdd (iConst 1) (iAdd (iConst 1) (iConst 1))), | |
E (iAdd (iAdd (iConst 1) (iConst 1)) (iAdd (iConst 1) (iConst 1)))] | |
main :: IO () | |
main = do | |
putStrLn "transform:" | |
demo simplify exs | |
putStrLn "futu:" | |
demo simplify' exs | |
where demo :: (Term Sig :-> Term Sig) -> [E (Term Sig)] -> IO () | |
demo f xs = mapM_ putStrLn $ runE (show . f) <$> xs |
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